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IM Geo.6.17 Practice: Lines in Triangles

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

The 3 lines , , and  intersect at point . Find the coordinates of . Verify algebraically that the lines all intersect at .

Triangle  has vertices at , , and . Kiran calculates the point of intersection of the medians using the following steps:

  1. Draw the triangle.
  2. Calculate the midpoint of each side.
  3. Draw the medians.
  4. Write an equation for 2 of the medians.
  5. Solve the system of equations.
Use Kiran’s method to calculate the point of intersection of the medians.

Triangle ABC and its medians are shown.

Write an equation for median .

Given  and , find the point that partitions segment  in a  ratio.

A quadrilateral has vertices , , , and . Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square. Do you agree with either of them? Show or explain your reasoning.  

The image shows a graph of the parabola with focus  and directrix , and the line given by . Find and verify the points where the parabola and the line intersect.

For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Write 2 equivalent equations for a line with -intercept  and -intercept . 

Parabola A and parabola B both have the line  as the directrix. Parabola A has its focus at  and parabola B has its focus at .Select all true statements.

Select all that apply
  • A
  • B
  • C
  • D
  • E
Check my answer (3)

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